This follow-up is slighlty aside the subject line of the mailing list, but

as a geologist, this is the only statistically-flavoured one I am

subscribed to. Therefore :

Federico Pardo <

federico.pardo@...> said:

> Having N samples, and then n degrees of freedom.

> One degree of freedom is used (or taken) by the mean calculation.

> Then when you calculate the variance or the standard deviation, you only

> have left n-1 degrees of freedom.

Apart a rigorous calculation I am aware of that in this very case (cf.

Peter Bossew's contribution on the same thread, that details it), gives a

proof for this rule-of-thumb, what more or less rigourous statistical

developments gives consistance to it ?

I mean, for the empirical correlation coefficient,

rhoXiYi = SUM_i=1..N( (x_i - mx).(y_i - my) / sx / sy ) / WHAT_NUMBER

Must WHAT_NUMBER be, for a kind of unbiased estimate ("a kind of" meaning

"with some eventual Fisher z-transform"...):

* N for simplicity,

* N-2 as I have most frequently seen in books that dare give this formula

(N points, minus 1 for position and 1 for dispersion ?),

* or 2N-4 -- 2N for the (x_i,y_i), minus 4 for {mx,my,sx,sy} -- as a

strict application of the rule-of-thumb seems to suggest ?

And what about, when fitting for instance a 3-parameter non-linear

function, reducing the number of degrees of freedom, to N-3 (number of

points, minus one for each function parameter ? I have never read any kind

of explanation to support it, though it seems widely

Thanks in advance for enlightments or simply tracks for other resources of

explanations.

-- Éric L.